What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature $$T$$?

According to the equipartition theorem, each degree of freedom of a gas molecule contributes $$\frac{1}{2}k_BT$$ to the average energy.

A monoatomic gas (like He, Ne, Ar) has only translational degrees of freedom. Since there are 3 translational degrees of freedom (motion along $$x$$, $$y$$, and $$z$$ axes), the average kinetic energy per molecule is:

$$\langle E \rangle = 3 \times \frac{1}{2}k_BT = \frac{3}{2}k_BT$$

This is the well-known result for the average thermal energy of a monoatomic ideal gas molecule at temperature $$T$$.